Maximum product of spacings prediction of future record values

Volovskiy, Grigoriy; Kamps, Udo

doi:10.1007/s00184-020-00767-1

Cited by 11 publications

(6 citation statements)

References 24 publications

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“…where ( Ri ) ∞ i=1 is the sequence of upper record values in an iid sequence of standard exponential random variables. Reasoning as in Volovskiy and Kamps [14], we conclude that…”

Section: Point Predictionsupporting

confidence: 56%

“…Among others, Kaminsky and Rhodin [12] presented the maximum likelihood predictor (MLP) and Volovskiy and Kamps [13] introduced the maximum observed likelihood prediction (MOLP). Based on a Pareto distribution, the MLP and MOLP for upper record values were shown in Volovskiy and Kamps [14]. However, both methods share the disadvantage that neither the next upper nor the next lower record value can be predicted reasonably, since the methods lead to the last record as predictor of the next one.…”

Section: Point Predictionmentioning

confidence: 99%

“…Moreover, there are some Bayesian results for estimation and prediction in the upper record Pareto setting in Ahmadi and Doostparast [16], Madi and Raqab [17] and Raqab et al [15]. For further references, we refer to Volovskiy and Kamps [13] and Volovskiy and Kamps [14].…”

Section: Point Predictionmentioning

confidence: 99%

“…We applied the maximum product of spacings prediction (MPSP) procedure for lower record values along the lines of Volovskiy and Kamps [14] for upper record values. The idea underlying the MPSP method is to apply a transformation to the sequence L = (L 1 , .…”

Section: Point Predictionmentioning

confidence: 99%

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Statistical Prediction of Future Sports Records Based on Record Values

Empacher

Kamps

Volovskiy

2023

Stats

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Point prediction of future record values based on sequences of previous lower or upper records is considered by means of the method of maximum product of spacings, where the underlying distribution is assumed to be a power function distribution and a Pareto distribution, respectively. Moreover, exact and approximate prediction intervals are discussed and compared with regard to their expected lengths and their percentages of coverage. The focus is on deriving explicit expressions in the point and interval prediction procedures. Predictions and forecasts are of interest, e.g., in sports analytics, which is gaining more and more attention in several sports disciplines. Previous works on forecasting athletic records have mainly been based on extreme value theory. The presented statistical prediction methods are exemplarily applied to data from various disciplines of athletics as well as to data from American football based on fantasy football points according to the points per reception scoring scheme. The results are discussed along with basic assumptions and the choice of underlying distributions.

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“…where ( Ri ) ∞ i=1 is the sequence of upper record values in an iid sequence of standard exponential random variables. Reasoning as in Volovskiy and Kamps [14], we conclude that…”

Section: Point Predictionsupporting

confidence: 56%

Section: Point Predictionmentioning

confidence: 99%

Section: Point Predictionmentioning

confidence: 99%

Section: Point Predictionmentioning

confidence: 99%

See 2 more Smart Citations

Statistical Prediction of Future Sports Records Based on Record Values

Empacher

Kamps

Volovskiy

2023

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Self Cite

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“…Recently, the MPS technique has attracted great attention in data analysis due to its potential advantage over the classical ML procedure. For instance, Singh et al [21,22], Shao [23], El-Sherpieny et al [24], Volovskiy and Kamps [25], Kawanishi [26] have discussed the MPS method under various data types when the lifetime distributions were the Weibull, power Lomax, generalized inverted exponential, generalized power Weibull, Lindley and generalized Rayleigh models, respectively. Anatolyev and Kosenok [27] studied the invariance property of the MPS and stated that the MPSEs have more efficient properties than the MLEs for skewed distributions or in small sample cases for heavy-tailed distributions.…”

Section: Introductionmentioning

confidence: 99%

Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples

Wang

Dey²,

Tripathi

2022

Mathematics

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This paper explores statistical inferences when the lifetime of product follows the inverse Nakagami distribution using progressive Type-II censored data. Likelihood-based and maximum product of spacing (MPS)-based methods are considered for estimating the parameters of the model. In addition, approximate confidence intervals are constructed via the asymptotic theory using both likelihood and product spacing functions. Based on traditional likelihood and the product of spacing functions, Bayesian estimates are also considered under a squared error loss function using non-informative priors, and Gibbs sampling based on the MCMC algorithm is proposed to approximate the Bayes estimates, where the highest posterior density credible intervals of the parameters are obtained. Numerical studies are presented to compare the proposed estimators using Monte Carlo simulations. To demonstrate the proposed methodology in a real-life scenario, a well-known data set on agricultural machine elevators with high defect rates is also analyzed for illustration.

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Classical and Bayesian inference of Cpc$\mathcal {C}_{pc}$ for Wilson–Hilferty distribution under progressively first‐failure type‐II censoring samples

Al‐Mosawi,

Dey

2024

Quality & Reliability Eng

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This study uses two frequentist approaches and the Bayesian method of estimation using progressively first‐failure type‐II censored data to estimate process capability index (PCI), , for the Wilson–Hilferty (WH) distribution. A competitive maximum product of spacing (MPS) method for estimation of is proposed in the frequentist method as an alternative to conventional likelihood (LK)‐based estimation. We have also taken into account the PS function in the Bayesian setup as an alternative to the conventional LK function, and both LK and PS‐based Bayesian estimates are given for . Further, the Bayes estimates are evaluated by applying Tierney–Kadane (TK) approximation method and Markov chain Monte Carlo (MCMC) method with the help of both LK and PS functions and Jeffrey's prior. Additionally, the approximate confidence intervals based on the suggested frequentist techniques as well as the Bayes highest posterior density (HPD) credible intervals are built for the index . In addition, two bootstrap confidence intervals are obtained. In the simulation exercise, the performance of the Bayes and traditional estimates of is assessed in terms of their mean squared errors, and the average width and coverage probabilities of the CIs and HPD intervals are compared. An actual data set from the electronic industries is reanalyzed in order to show the efficacy of the proposed index and estimation methodology.

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Maximum product of spacings prediction of future record values

Cited by 11 publications

References 24 publications

Statistical Prediction of Future Sports Records Based on Record Values

Statistical Prediction of Future Sports Records Based on Record Values

Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples

Classical and Bayesian inference of Cpc$\mathcal {C}_{pc}$ for Wilson–Hilferty distribution under progressively first‐failure type‐II censoring samples

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